ES2200982T3 - SIMILAR PROCEDURE TO CORDIC, OF COMPLEX VALUES, FOR SIGNAL PROCESSING TASKS. - Google Patents

Abstract

A procedure similar to CORDIC of complex value for signal processing tasks that can be reduced to a minimum square problem with at least one linear secondary condition, - in which the linear secondary condition is included in the minimum square problem to be solved, formulated as a partially Gaussian elimination with the help of a Schur complement, - in which the minimum square problem is solved by means of a QR dissection by an algorithm, using linear Gaussian transformations and Givens rotations of the circuit, and - in which the algorithm is executed on a higher triangular field of processors and the secondary conditions are taken into account at least in one stage of work within the field of processors.

Description

Similar procedure to CORDIC, of securities complex, for signal processing tasks.

The invention relates to a process SCORDIC of complex values for tasks of processing signals according to claim 1 of the patent as well as to a radio communication system for the realization of a This type of procedure.

The increasing number of applications in time real in the field of wireless communication, for example radio mobile of the third generation according to the UMTS Standards (UMTS: Universal Mobile Telecommunications System), makes the development of algorithms and architectures for processing Signal parallel. Most algorithms and structures known presuppose in this case the entry of real data. This especially applies to the case in which the architectures they must enable a VLSI implementation. The cases with data complexes are usually covered with the help of facilities normalized, for example by applying four real multiplications for the realization of a complex multiplication. The process complex data acquires, however, growing importance in many practical applications, such as in adaptive ray formation, especially here of the curve address feature that can be adjusted electronically from a field of antennas, or from the detection of several users.

The provisions of computers for forms of MVDR adaptable beams (MVDR: minimum variance distortionless response = undistorted response of minimum variance) essentially implement the solution of a value problem complex by means of the least squares method (least squares problem), which is achieved through the inclusion of a or of several secondary conditions in the given problem of minimization In this case, in the MVDR, it is minimized the variance of the output signal, which corresponds to the power mean, while maintaining the additional condition in the sense that the signal must be received not falsified for a direction of incidence determined, that is, without amplification or attenuation. In addition, a direct calculation of the signal is implemented output by means of a final multiplication of the signals of output of the right sides by the square root of the factor of transformation. Calculations for the inclusion of conditions secondary are not implemented in this case in these matrices of processors or processor fields, but are carried out in a preprocessing stage. The processor fields they consist entirely of processor cells, which calculate circular rotations (diagonal cells) or apply circular rotations (non-diagonal cells). It is known ways of MVDR adaptable beams, for example, from "Pipelined CORDIC Based QRD-MVDR Beamforming ", J. Ma, K. K. Parhi,  Ed. F. Deprettere, Proc. IEEE Int. Conf. On Acoustincs Speach, Signal Processing, pages 3025-3028 Seatle (USA), 1998 (QDR: QR dissection of a matrix). In the case of processor fields expanded, MVDR beam formation is done with several linear secondary conditions.

In "Annihilation-Reordering Look-Ahead Pipelined Cordic-Based RLS Adaptive Filters And Their Applications To Adaptive Beamforming ", Jun Ma et al., IEEE Transactions On Signal Processing, August 2000, IEEE, USA Vol. 48, No. 8, pages 2414-2431, XP002166872 ISSN: 1053-587X, rotation techniques of Givens in adaptable filters.

To execute value transformations complexes, are formulated in a factored form, this factorization it is composed in a corresponding way by transformations linear and circular of real value, and phase turns are incorporated of complex numbers in the transformation. These twists of phases they can be transmitted in the complex plane also over circular transformations Therefore, the transformations complex can be transmitted over a number of transformations real, such as a complex multiplication, which can be express through four real multiplications. However, using this factorization it is possible to formulate a scheme of factored rotation for a complex transformation, that is, one of the phase turns is accumulated in a diagonal matrix, which accompanies the corresponding included matrices during the algorithm. This corresponds to the basic idea of rotations. factored factors, in which the scale factors are preserved in a diagonal matrix. The diagonal matrix is compensated at the end of calculations. In this way the number of rotations is reduced real necessary, so that only two are necessary real rotations, to activate the imaginary portions of the complex values included.

As explained, the entire triangular field superior processor for MVDR beam formation with Several secondary conditions can be executed based on processor cells, which execute complex 2x2 transformations linear and circular. These transformations are designated as 2x2 linear and circular real transformations. Each real transformation is executed using a CORDIC processor linear and a circular CORDIC processor, respectively (CORDIC: Coordinate Rotation on Digital Computer). In the procedure CORDIC, the rotation of a vector of two elements is done with the help of simple scrolling and adding operations. The accumulated phase factors in the diagonal matrix are compensated through the final linear transformations to Direct calculation of the output signal.

The present MVDR beam former, which is here it refers especially to a field of curved antennas electronically adjustable directional feature, in which they take into account several groups of secondary conditions, find application in a digital modulated signal, for example a 4-QAM signal (4-QAM: Modulation of the Amplitude in Quadrature with 4 points in the signal space). The simulations show that the necessary calculation expense especially considering the accuracy of the approach and scale formation depends largely on the conditions application-specific, for example SNR (SNR: signal to noise ratio, distance between signal and noise or ratio between signal and noise).

A usual scenario comprises M elements sensors, without directional effect, which are arranged in a plane in my positions. The antenna array or the antenna field receive a mixture of desired signals, which must be decoded, of unwanted interference signals from unknown addresses and background noise, which is equal to the average of all addresses. In such a scenario represented in the figure 1 it must be taken into account that from the point of view of the signal of reception S_ {1} (t), the second signal S_ {(}) it also represents a source of interference, in which know the direction of incidence, instead the signal S_ {3} (t) must represent a source of interference with An unknown arrival address. For simplification it is assume that the direction of propagation is the same on each sensor and the shapes of the waves are flat, so that you can accept the approach of the far field. Output signals individual sensors xi (t) are present as a signal  of complex baseband, taking into account that Received signals are usually modulated signals of some way, which are converted into equivalent low pass signals. Therefore, a narrow band approach can be accepted, that is, that each antenna element receives the same signal, but This with a delay of time. The equivalent low pass signal in a sensor i can be written as

(1) x_ {i} (t) \ = \ \ tilde {x} \ (t) \ exp \ (-j2 \ pi f_ {c} \ tau_ {i}) \ + \ n_ {i} (t),

where x (t) is the baseband signal complex in a virtual reference sensor element, which is arranged at the origin of the antenna coordinate system, which is represented in figure 1, \ tau_ {i} represents the delay of signal time on a sensor i with respect to the sensor reference, f_ {c} represents the carrier frequency and n_ {i} (t) represents the white noise of Gauss. For the therefore, for a complete description of figure 1 two are needed equations A more compact annotation is possible through the combination of exp expressions, which belong to each antenna and to each known propagation direction, in a matrix N x M C, where N is the number of the known directions of the signals. The matrix is defined as follows way:

one

where \ phi_ {i, k} = applies -2 _ {\ pi} f_ {c} \ tau_ {i, k}. The index k corresponds to the k input address for a default field geometry, and in the case of predetermined input addresses, they can be Easily calculate time delays \ tau_ {i, k} through of projection considerations. Discrete signals x_ {i}, (n) they are considered as output signals of frontal ends analogues or front connections with a front end by sensor. The details in this regard are explained in relation to the following embodiment example. The scanned signals are arranged in a matrix n x M X:

two

where n is the quantity or the number of sampling values, which are taken on each antenna. Through the weighting of the output signals of the sensors or of the starting values with complex factors w_ {m}, the sum of these products provides a spatial filter, a so-called trainer of mallets or beamformer. Under the fact that each factor weighting w_ {i} = [W_ {1}, ..., W_ {M}] {T} belongs to a desired output signal e_ {i}, a signal matrix E = [e_ {1}, e_ {2} ... e_ {1}], which contains filter output values, where L \ leq N.

The technique aimed at the objective for forecasting of the addresses consists in requiring that the desired signals, however noise and noise are suppressed interference signals, which affect from all directions. This leads to the following representation of Minimum Squares:

(4) min_ {W_ {1}} || \ e_ {i} = Xw_ {i} ^ {\ textstyle *} \ || ^ {2 -} _ {2} \ for \ i \ \ in [1, L] under \ CW ^ {\ textstyle *} = B,

         \ newpage
      

where L is the number of the output signals desired and B designates the amplification matrix, especially the profit matrix Most of the time, the elements in the matrix N x K B are taken from the amount {0,1}; 0 for a deletion of the interferences, 1 for a unit amplification of the Information signal The weighting matrix W consists of again for vectors w_ {i}, so that [W_ {1} W_ {2} ..., W_ {L}]. In this way, with the criteria of Squares Minimum, try to minimize the output power of the beamformer and at the same time meet the conditions high schools. For the scenario depicted in Figure 1, it is they obtained N = 2 secondary conditions for the two directions of known signals s_ {1} (t), s_ {(}), of ways that C: 2xM, B = I_ {2} is applied, to obtain E = [e_ {1} e_ {2}].

In the procedures known so far, that run an MVDR beam formation algorithm over a field of processor, conditions are not calculated at the same time secondary within the processor field, but they are held in account in a separate preprocessing stage. Thus, a correspondingly high expense is necessary both in terms of hardware as well as programming, especially to be able to perform a data detection in the case of using Several antennas

The purpose of the invention is to improve a CORDIC procedure of complex values for tasks of signal processing as well as a communication system for radius for the conversion of such a procedure.

This task is solved through a CORDIC procedure of complex value with the characteristics of claim 1 of the patent or through a system of radio communication for performing a procedure this type with the characteristics of claim 7 of the patent. Advantageous configurations are subject to dependent claims.

According to the invention, using the complement of Schur formulates the inclusion of secondary conditions linear in the problem of minimization as a partial Gaussian elimination. The problem of minimum squares that As a result, it is solved by means of a QR dissection. Even the final multiplication for the direct calculation of the output signals can be formulated as a linear transformation using the complement of Schur. In this way, you get a implementation, which is based entirely on linear transformations Gaussians and Givens circular rotations and runs through of a superior triangular field of processors.

Such a procedure enables especially the complete processing of value signals complex in uniformly constituted cells based on Real CORDIC. The procedure is carried out in this case in a field of processors, being incorporated in the calculation at the same time the secondary conditions and suppressing, therefore, a separate preprocessing stage.

A procedure is also advantageous, which allows the conservation of complex phase factors in a diagonal matrix as proposed.

The procedure offers especially the possibility of very simple hardware execution especially in a communication system, since the cells they have, on the one hand, a structure very similar to each other and, for On the other hand, through CORDIC execution they should only perform displacement and addition operations.

An example of realization with the help of drawing. In this case:

Figure 1 shows a scenario with four sensor elements, with two signals S_ {1} (t) and S_ {2} (t) bearers of information from addresses different and with an interference signal or signal disturbance S_ {3} (t) from an unknown address.

Figure 2 shows complex CORDICs, being (a) a linear evaluation, (b) a linear application, (c) a circular evaluation and (d) a circular application, where the blocks  they are composed of real linear and circular CORDIC modules, which are operated in a type of vector operation and of rotation.

Figure 2a shows an explanation of the Symbols used in this case.

Figure 3 shows (a) a cell of multiplication according to the CORDIC principle and (b) and (c) cells triangular, which perform a Gamma calculation and an accumulation of the rotations of the phases.

Figure 4 shows a complete field of processors

Figure 5 shows a table for the representation of the frequency of binary errors during use of approximation rotations similar to CORDIC with a  compensation of the scale factor, where each processor cell Actual value CORDIC executes the same number of CORDIC iterations (rotations µ), and additionally the frequency of errors binaries in the case of the use of exact rotations.

Figure 6 shows a directional diagram resulting from the processor field., Three signals from different addresses Two signals must be suppressed, and must receive the -90º signal with an amplification of 0 dB. Additionally, all incoming signals are disturbed by noise (distance between signal / noise 8 dB per antenna). The answer of the amplitude is calculated from a (\ xi) = 20 log_ {10} | [e ^ {j \ varphi 1 (\ xi)}, ..., e ^ {j \ varphi M (\ xi)}] W_ {1} |.

Figure 7 shows the representation of the binary error frequency versus number of rotations \ mu (distance between signal / noise = 8 dB), where the dashed line shows the frequency of binary errors in the case of rotations exact; Y

Figure 8 shows a schematic structure of A base station.

For the explanation of an example of realizations firstly explains the solution of the problem of Optimization affected by secondary conditions. A principle of solution of the optimization problem with secondary conditions is to formulate the problem as a square problem Minimum (Least Square Problem: Minimum Squares Method (of error) no marginal conditions. With C = [C_ {C} {2}], W T = [W T 1 W T 2] and X = [X 1 X 2], where a * = [* 1 * 2] designates the division of an array * in two sub-matrices, where the first one presents N columns, you can write the equation for secondary conditions like

(5) C_ {1} W_ {1} ^ {\ textstyle *} + C_ {2} W_ {2} {\ textstyle *} + B

The resolution with respect to the matrix W1 gives as Outcome

(6) W_ {1} {\ textstyle *} = C_ {1} (B-C_ {2} W_ {2} {\ textstyle *})

It results

XW_ {1} ^ {\ textstyle *} = (X_ {2} - X_ {1} C_ {1} ^ {- 1} C_ {2}) w_ {2} ^ {\ textstyle *} - (-X_ {1 C_ {-1} B)

To this end they can be solved with

(7) \ overline {X} 2 = X_ {2} - X_ {1} C_ {1} ^ {- 1} C_ {2} \ \ y \ \ \ overline {B} _ {2} = -X_ {1} C_ {-1} B

square problems minima

(8) min_ {W_ {2}} || x_ {2} w * {2} - \ overline {B} 2 || ^ 2 -} 2

to get W_ {2} and then calculate W_ {1} from (6). At another stage the signals of desired output through from

(9) E = XW *

Especially regarding an execution parallel hardware is advantageous to incorporate the stages, which are included in the solution of the problem of minimum affected squares by secondary value, that is, from the equations in (6), in (7), in (8) and in (9), in a process of matrix generation triangular The matrix M (n + N) x (M + K) is defined as:

2. 3

The application of a sequence of Gaussian transformations G_ {pq} (s) on the matrix M, where G_ {pq} (s) solves the element m_ {pq}, so that C_ {1} is taken to the upper triangle configuration and X_ {1} resolves completely, leads to:

24

where R_ {1} is an upper triangular matrix and the matrix n x (M-N + K) \ lfloorX_ {2} B_ {2} \ rfloor is the complement of Schur de M. It should be noted that the transformations can be selected for that the diagonal elements of R_ {1} are values real.

The problem of minimum squares, which is connected to the lower left block, it can be resolved to through the QR dissection of \ lfloorX_ {2} \ rfloor, of such way that applies

\ bar {X} 2 = [Q_ {Q} {s}] \ lfloor {R_ {2}} {0} \ rfloor

where [Q_ {2} Q_ {s}] represents an array unitary. The necessary unitary transformation is constituted by rotations of Givens J_ {pq} (\ theta). The definition of the matrix

[P H 1 P H] = BH2 [Q_ {2} Q_ {s}]

and the application of a sequence of rotations of Givens on M 'shows that the partial process of triangle formation of (11) is continued through transformations unitary:

25

As before, Givens rotations are they can select so that the diagonal elements of R_ {2} Be real values. Through the application of the equations above you can determine the output signals really without an explicit calculation of W.

(13) E = XW * = Q_ {2} R2_ W_ {2} {*} - \ overline {B} 2.

Since R_ {2} W_ {2} ^ {*} is applied = P_ {2} and B_ {2} = Q_ {P} {2} + Q_ {S} P_ {s}, gets

(14) E = -Q_ {S} P_ {s}.

For the realization of the algorithm a matrix of processors or a field of processors. Since the entire algorithm is formulated with a view to training triangular of the matrix M, can be executed in a triangular of processors

Since the signals are of complex values, processor cells must manipulate value data complex. In the case of a usual execution, the cells must essentially perform multiplications and sums. However, the secondary cells, which calculate linear transformations and unitary, calculate in a corresponding way square roots and divisions Due to their technical complexity of calculation, these Calculations require more time than multiplications. For solve this problem, the structure is considered below Inside the processor cells.

Next, the complex modules are reduced CORDIC to real CORDICS, that is, to procedures, which execute through simple scrolling and adding operations the Rotation of a vector of two elements. To enable it, it first formulate complex rotations in one way factored It is clear that the general complex modules are they can simplify in the case of using these in a MVDR beamformer. With a view to unit rotations, it consider first a 2x2 Tu matrix, which is applied on a vector v = [ra] T, where both r and also a they represent complex numbers, that is,

r = \ Re ^ {\ {r \} + j} \ Im ^ {\ {r \}} and a = \ Re ^ {\ {a \} + j} \ Im ^ {\ {a \}}. Then T_ {u} is defined through

5

where

S = al \ sqrt {| r | ^ {2} + | a | ^ {}}, c = r l \ sqrt {| r | ^ {2} + | 2a0 | ^ {2}}

and therefore it apply:

T_ {u} \ nu = [\ sqrt {| r ^ {2} | ^ {2} + | a | ^ {2}} 0] ^ {T}

Next, \ varphia and \ varphir are the phase angles of a and r, respectively. Now you can dissociate T_ {u} in four matrices:

3

where I know apply:

breast \ delta = \ frac {| a |} {\ sqrt {| r | ^ {2} + | a | ^ {2}}} and cosine \ delta = \ frac {| r |} {\ sqrt {| r | ^ {2} + | a | ^ {2}}}

If the complex vector v of two is now described elements through a v- vector of four elements with real elements where

(17) v = [\ Re \ {r \} \ Im \ {r \} \ Re \ {a \} \ Im \ {a \}] ^ {T}

complex transformation can be formulated factored into equation (16) in expressions with 4 real transformations as follows. The application of rotations of Givens

6

Y

7

on the vector v- corresponds to the multiplications

re ^ {- j \ varphi ^ {r}} \ o \ ae ^ {- j \ varphi ^ {a}}

In the same way, the application of the matrix

8

on the vector 0 v- corresponds to the application of T_ {3z} (δ) over v. So far they have replaced three of the four complex factors in the equation (16). The remaining factor [gamma] can be expressed also as a real rotation. However, it is advantageous not perform this rotation in combination with the others but delay it this stage. Phase shifts are supposed to γ \ varphi are not performed with the other transformations, that is, there is a 2x2 diagonal matrix remaining, which is consisting of factors of independent phases e ^ j \ varphi 1} and e ^ j \ varphi 2. To perform the next cancellation stage in the sequence of rotations of Givens, you have to perform a unit transformation, which is predetermined in the equation (fifteen). From this, it follows that you have to calculate

9

where I know apply

22S = \ frac {| a | e ^ {j (\ varphi a (+ \ varphi 2)}} {\ sqrt {| r | ^ {2} + | a | ^ {2}}} und c = \ frac {| r | e ^ {j (\ varphi r + \ varphi 1)}} {\ sqrt {| r | ^ {2} + | a | ^ {2}}}

After some algebraic transformations, from this it follows

eleven

The important point is that the factors of phases can be accumulated in the guide diagonals matrix. From this way phase compensation can be performed in one stage of final transformation and should not be calculated in each cell of the processor. This is similar to the principle that applies to rotations. factored, where rotational scale formations are accumulate in a matrix of attached diagonals. Since T_ {u} according to (16) it can be considered as factored rotation, it can be correspondingly manipulate the first matrix of diagonals In opposition to factored rotations, it is not necessary compensation of the diagonal matrices during the algorithm to avoid an overflow, since the matrices of diagonals \ gamma _ {\ varphi} only contain factors of phases

The rotations are considered below linear In a manner similar to unit rotations, it is possible to write a complex linear rotation as a product of four matrices, which are suitable for real representation. In the linear case, the 2x2 T1 transformation matrix, which is apply on the vector v = [r a] ^ {T}, to solve its second component is given through

12

Similarly, a dissection of T_ {1} as

13

Through the comparison of expressions in equation (25) with the expressions in equation (16) can be establish that the transformations T_ {1} and T_ {2} appear in both cases. However, the unitary transformation T_ {3z} is can substitute for a linear transformation T 31. Is complex transformation can be formulated again as a matrix 4x4 transformation:

14

As in equation (16), a next multiplication by \ gamma \ varphi, which corresponds actually to a correction of the phases of the two elements of T_ {31}, T_ {T} {T} {V}. As stated above, it is possible to inscribe the turns of the phases in a matrix of diagonals, in other words, it is possible to accumulate them in a separate diagonal matrix.

A form of exemplary embodiment. In the event that now all real transformations are replaced by CORDIC blocks, complex CORDIC cells appear from the factored representations. The complex blocks, which are based in real CORDIC cells, they are represented in figure 2. In in this case, the diagonal values of R_ {1} and R_ {2}, respectively, they are real values. Therefore, they can be omitted several real CORDIC cells in complex CORDIC blocks precedents These blocks are represented with dashed lines. in figure 2. The complete field of processors, which is based on CORDIC, is represented in figure 4. The two series of processors on the upper side carry out the removal partial Gaussian while the cells in the two lines arranged below carry out the QR dissection. Here the partial Gaussian transformations for the generation of matrix

\hskip0.5cm

a \ partir \ de

\hskip0.5cm

[C_{1}C_{2}B]\ lfloor \ tilde {C} \ tilde {B} \ rfloor = [R_ {1} \ overline {C} _ {2} \ \ overline {B} _ {1}]

 \ hskip0.5cm 

from

 \ hskip0.5cm 

[C 1 C 2 B]

are made in a second block of DOA processing (DOA: direction of arrival / address of reception). DOA algorithms estimate signal directions Incoming Under the high resolution capacity with respect to to the algorithms for estimating the address you can achieve improved power capacity through calculation of transformations, with high accuracy. Since the record values at the top of the field should not be updated at each sampling stage, because the address of Signal input (DOA) is modified relatively slow with respect to time, runtime is not critical of the estimator of the address.

The values C i, k and b_ {i, jk} are assigned then to the linear cell records of the processors This procedure increases the accuracy of secondary conditions in the case of the use of transformations approximate, based on CORDICs. However, we must indicate that the processor field works with a certain accuracy for all CORDIC modules, that is, with a fixed number of rotations µ for each CORDIC module.

The column of the processor field, which is constituted by triangular cells, it carries out the calculation of Gamma factor, which is deduced from equation (14), as also the compensations of the phases y _ {\ varphi} e y _ {\ varphi one}. The corresponding cells are represented in the figures 3 (b) and 3 (c).

The γ factor compensation, which is seduces from equation (14), it is not executed as a usual multiplication cell, cone through blocks, which they present an internal structure similar to the rest of the field. TO then b_ {i} and c are considered complex numbers arbitrary Through the formal application of a Gaussian transformation about

fifteen

c can be solved, to calculate the complement from Schur de M, is tell,

16

As is evident, the complement of Schur corresponds to product c [b1, b2, ...]. Therefore, the multiplications could be executed as a calculation of the transformation and an application of the transformation. In one way more advantageous, it can be used for a vectorization the same cell used in the upper part of the field (figure 2 (a)). In addition, the application cell, which is represented in Figure 3 (a), has a structure very similar to the cell hexagonal.

The results of the simulation. In the following simulations it is assumed that signals to be decoded are 4-QAM modulated signals. The parameters are chosen in such a way that a scenario is represented with M = 5 antennas and 3 input signals. The antennas are evenly distributed in a circular arrangement, where the distance between the neighboring sensors is set in half of the wavelength.

The first simulation experiment has been made with two equal signals in terms of power, which impact from known directions under an angle of -90º and 63.4º, respectively. An interference signal with address unknown affects from 128.7º. Binary Error Frequencies that are deduced are represented in figure 5 as a function of the distance between signal / noise or as a relation between signal and interference. Processor cells work with a number different from CORDIC iterations. The results have been compared with a simulation test, in which rotations were used exact. It should be noted that already three rotations \ mu lead almost at the same frequency of binary errors as the calculation exact.

The following are the patterns of you either make the address diagrams that result from it, here of a system of antennas or a field of antennas. For determine the field address diagrams, the field registration cells after certain stages of simulation. As explained before the field description of processors, from this you can calculate the factor of inherent weighting. The resulting address diagrams are represented in figure 6. The directions of the signals and the interference signal or the directions of the signals of interference are represented by dashed lines. Although the curves have a different development, they meet the expectations. Both the address diagram calculated with accuracy as well as the address diagrams of the approximate solutions meet the secondary condition "amplification equal to one" in the sense of an MVDR criterion in an optimal way. In addition, the signal suppression of disturbance or of the known interference signal is very exact. Suppression of the unknown interference signal increases with the number of rotations µ.

For the characterization of the approximation, believes that a compromise between the quality of the output signal (BER): Bit error rate / binary error rate and expense Calculation has a moderate cost. In this regard, Figure 7 shows the power capacity profile of the field using approximate rotations similar to CORDIC with a compensation of scale factor. Gay to indicate that 4 rotations are enough to achieve the total possible power capacity.

For the application of the procedure, it is proposed the conditioning of base stations, such as the station base represented in figure 8, with several dipole antennas 2 in arbitrary spatial arrangement for the use of the field of 1 processors described. The data stream that can be obtained in this way it supplies a respective cell in the field of processors 1. The address information about the signals Useful and input interference signals is provided by a separate block of DOA arrival address, 3. In the outputs 4 from the user side of the processor field are find the complex N data streams, which represent the Information of the baseband of N incoming signals, for that input addresses are present. Therefore every output provides signals from an array of directed antennas of an optimal way about the issuer in the sense of the criterion MVDR

The triangular field 1 described above is preferably executed in an ASIC (ASIC: Application Specific Integrated Circuit = Specific Integrated Circuit of the Application) or FPGA (FPGA: Field Programmable Gate Array = module freely programmable logic, consisting of structures regular). This regular structure also enables the use of multiple processor systems. The units of rotation of the individual cells are preferably made by means of CORDIC blocks CORDIC blocks of complex value are returned in this case to CORDIC modules of real value. In principle, the field of processors 1 is suitable for processing any problem in complex signal processing, which can be attributed to a problem of minimum squares with secondary conditions. How Preferred example is mentioned an MMMSE receiver (MMMSE: Modified Minimum Mean Square Error = Minimum Mean Square Error Modified). MMSE designates a general criterion for the adjustment of filter coefficients, where the MMMSE receiver is used to CDMA transmission systems (CDMA: Code Division Multiple Access = Multiple Access by Code Division). CDMA is used, for example, in future mobile radio systems for transmission to via the radio interface, for example in UMTS (Universal Mobile Telecommunications System) or in other systems of the third generation with frequencies in the frequency band of approximately 2000 MHz. The modification allows in this case also the use in channels, which meet a statistic of Rayleigh

Claims (9)

1. Procedure similar to CORDIC of value complex for signal processing tasks that can be reduced to a minimum square problem with at least one linear secondary condition,

-

in which the linear secondary condition is included in the problem of minimum square to be solved, formulated as an elimination partially Gaussian with the help of a complement of Schur,

-

in which the Minimum square problem is solved by dissection QR by an algorithm, using Gaussian transformations linear and Givens rotations of the circuit, and

-

in which the algorithm is executed on a higher triangular field of processors and the secondary conditions are taken into account least in a work stage within the field of processors

2. Method according to claim 1, in the that a multiplication is formulated, following the solution of the minimum square problem, using Schur's complement As a linear transformation. 3. Procedure according to one of the preceding claims, wherein the phase factors complexes that occur in solving the square problem minimum are transferred to a diagonal matrix. 4. Procedure according to one of the preceding claims, wherein the algorithm is performed with the help of uniformly structured cells that are formed to real CORDIC base. 5. Method according to claim 4, in the that only diversion and addition operations are executed in the execution of the algorithm based on CORDIC. 6. Procedure according to one of the preceding claims, wherein the CORDIC blocks of complex value are reduced to real value CORDIC modules for the Algorithm realization. 7. Radio communication system for embodiment of the method according to one of the claims precedents,

-

in which the system Radio communication contains at least one station transmission and a reception station,

-

in which at least a reception station has a plurality of antennas (2) in an arbitrary spatial arrangement,

-

in which the reception station presenting a plurality of antennas contains the field of processors (1) structured in a way triangular and the latter has a plurality of entries for receive the antenna signals of the plurality of antennas (2) and a plurality of outputs (4) to emit the N data streams N complexes with baseband information of the N signals of antenna incidents.

8. A radio communication system according to the claim 7, wherein the plurality of outputs (4) of the field of processors (1) are coupled to an antenna receiver conventional individual (5). 9. A radio communication system according to the claim 7 or 8, wherein the receiving station contains an arrival address block (DOA, 3) that supplies address information on the incident useful signals and the  noise signals